Alice Walker has won awards and is known for her contributions to modern American literature as someone who gave a voice to African American women. Through novels, short stories, poetry, essays, and even children's literature, she has maintained a focus on many themes, including heritage, empowerment, and truth to self. "Everyday Use" is no exception.
In order to examine this short story for its "strengths" I encourage you to choose one theme (or subject) that is portrayed and examine it through Walker's use of different literary elements. Certainly, the point-of-view is noteworthy. Using the first person perspective (common of Walker) takes the reader directly into the heart and head of one of the main characters. As a result, the diction (or word-choice) and attitude (or tone) tend to be even more authentic. You could also add the use of figures of speech to your analysis. If you want to take a more broad approach, you might look at the difference between the characters, the conflicts, and the resolution to these conflicts.
I personally find it difficult to critique the weaknesses of a well-known, well-liked, highly respected, and widely published author like Alice Walker. To find weakness in any of her published works, to me, would be presumptuous, as I am by no means an expert. If your assignment dictates that you must speak about both strengths and weaknesses, you could always approach the weaknesses from your own thoughts and opinions. For example, you could discuss any part of the story that you didn't like, and why. You could also discuss anything that seemed particularly confusing. Perhaps the confusion will lead you to something you consider a literary weakness in the story.